$ \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\abs}[2][]{\left\lvert#2\right\rvert_{\text{#1}}} \newcommand{\ket}[1]{\left\lvert#1 \right.\rangle} \newcommand{\bra}[1]{\langle\left. #1\right\rvert} \newcommand{\braket}[1]{\langle #1 \rangle} \newcommand{\dd}{\text{d}} \newcommand{\dv}[2]{\frac{\dd #1}{\dd #2}} \newcommand{\pdv}[2]{\frac{\partial}{\partial #1}} $
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A subset $B\subseteq V$ is a basis for $V$ if
  1. $V=\text{span }B$
  2. $B$ is linearly independent
That is, a basis for $V$ is the minimal spanning set for $V$.

Concepts

If $S\subseteq V$ is linearly independent, then $S$ is a basis for $\text{span }S$.

Used In

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Hypothesis

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A subset $B\subseteq V$ is a basis for $V$ if
  1. $V=\text{span }B$
  2. $B$ is linearly independent
That is, a basis for $V$ is the minimal spanning set for $V$.

Concepts

If $S\subseteq V$ is linearly independent, then $S$ is a basis for $\text{span }S$.

Used In

Coming soon

Hypothesis

Coming soon

Results

Coming soon
FullPage
definition
concepts
used in
hypothesis
results
FullPage
definition
concepts
used in
hypothesis
results
A subset $B\subseteq V$ is a basis for $V$ if
  1. $V=\text{span }B$
  2. $B$ is linearly independent
That is, a basis for $V$ is the minimal spanning set for $V$.

Concepts

If $S\subseteq V$ is linearly independent, then $S$ is a basis for $\text{span }S$.

Used In

Coming soon

Hypothesis

Coming soon

Results

Coming soon
A subset $B\subseteq V$ is a basis for $V$ if
  1. $V=\text{span }B$
  2. $B$ is linearly independent
That is, a basis for $V$ is the minimal spanning set for $V$.

Concepts

If $S\subseteq V$ is linearly independent, then $S$ is a basis for $\text{span }S$.

Used In

Coming soon

Hypothesis

Coming soon

Results

Coming soon
FullPage
definition
concepts
used in
hypothesis
results